149 citations · 841 across the 44 of their papers we have counts for
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math.CO2008★ 12 cited
Parallel Chip-Firing on the Complete Graph: Devil's Staircase and Poincare Rotation Number
Lionel Levine
We study how parallel chip-firing on the complete graph K_n changes behavior as we vary the total number of chips. Surprisingly, the activity of the system, defined as the average…
math.CO2008★ 149 cited
Chip-Firing and Rotor-Routing on Directed Graphs
Alexander E. Holroyd, Lionel Levine, Karola Meszaros +3
We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present s…